How will having corns affect my child's long-term health?

Corns. Corns will not affect long-term (or short-term) health. However, they can be very uncomfortable.
Variable. The long term effects are similar to the short term effects if the corns are not treated. This includes potential for pain due to friction/rubbing of corn, including when wearing tight fitting socks or shoes, and redness and swelling around the corn. Other things to watch for are secondary infection, breakdown of the skin at site of corn (ulcer) and formation of a blisters (due to friction).
Corns are local. Corns are a local foot problem and there for will effect walking, and if not treated may cause difficulty with feet,knees and hips. See a podiatrist for treatment.